Methods and systems for identifying and mapping cardiac activation wavefronts

ABSTRACT

A map of cardiac activation wavefronts can be created from a plurality of mesh nodes, each of which is assigned a conduction velocity vector. Directed edges are defined to interconnect the mesh nodes, and weights are assigned to the directed edges, thereby creating a weighted directed conduction velocity graph. A user can select one or more points within the weighted directed conduction velocity graph (which do not necessarily correspond to nodes), and one or more cardiac activation wavefronts passing through these points can be identified using the weighted directed conduction velocity graph. The cardiac activation wavefronts can then be displayed on a graphical representation of the cardiac geometry.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.15/252,498, filed 31 Aug. 2016 (the '498 application), now pending,which claims the benefit of U.S. provisional application No. 62/213,434,filed 2 Sep. 2015 (the '434 application). The '498 and '434 applicationsare hereby incorporated by reference as though fully set forth herein.

BACKGROUND

The instant disclosure relates to electrophysiological mapping, such asmay be performed in cardiac diagnostic and therapeutic procedures. Inparticular, the instant disclosure relates to systems, apparatuses, andmethods for identifying and mapping cardiac activation wavefronts.

A conduction velocity (“CV”) map in an intra-cardiac navigation andmapping system displays the direction and speed of the electricalconduction at a given map point. The CV map can be computed by gatheringlocal activation times (“LAT”) of neighboring points, or by othermethodologies.

Given a CV map, it can also be of interest in an electrophysiology studyto identify different wavefront patterns. Multiple wavefront patternsmight occur during cardiac activations, including, for example,collision, focal, re-entry, and rotor. The identification andinterpretation of these wavefronts can help analyze mechanisticproperties of a broad range of electrophysiological pathologies. Tostudy these wavefront patterns, however, one must first be able toidentify them (e.g., as a group of conduction velocity vectors in the CVmap associated with the same source).

BRIEF SUMMARY

Disclosed herein is a method of mapping a cardiac activation wavefront,including the steps: receiving a geometry of at least a portion of acardiac surface, the geometry including a plurality of nodes; receivingelectrophysiology data for the portion of the cardiac surface, theelectrophysiology data including conduction velocity data; assigning aconduction velocity vector to each node of the plurality of nodes usingthe conduction velocity data, thereby creating a plurality of conductionvelocity vectors; defining a plurality of directed edges connecting theplurality of nodes, thereby creating a directed conduction velocitygraph; assigning a weight to each directed edge of the plurality ofdirected edges in the directed conduction velocity graph, therebycreating a weighted directed conduction velocity graph; and identifyinga cardiac activation wavefront using the weighted directed conductionvelocity graph.

The step of assigning a conduction velocity vector to each node of theplurality of nodes using the conduction velocity data can includeinterpolating the conduction velocity data to assign each conductionvelocity vector to an associated node of the plurality of nodes.

The step of defining a plurality of directed edges connecting theplurality of nodes can include repeating, a plurality of times:selecting a first node within the plurality of nodes, the first nodehaving assigned thereto a first conduction velocity vector; selecting asecond node within the plurality of nodes, the second node havingassigned thereto a second conduction velocity vector; defining a firstvector connecting the first node to the second node; defining a secondvector connecting the second node to the first node; computing a firstangle between the first conduction velocity vector and the first vector;computing a second angle between the second conduction velocity vectorand the second vector; defining a directed edge from the first node tothe second node when the first angle is less than 90 degrees; anddefining a directed edge from the second node to the first node when thesecond angle is less than 90 degrees.

In some embodiments, the step of assigning a weight to each directededge of the plurality of directed edges in the directed conductionvelocity graph can include, for each directed edge, assigning a weightbased upon a first conduction velocity vector assigned to a first nodeof the respective directed edge and a second conduction velocity vectorassigned to a second node of the respective directed edge.

In other embodiments, the step of assigning a weight to each directededge of the plurality of directed edges in the directed conductionvelocity graph can include, for each directed edge, assigning a weightbased upon a time required to travel between a first node of therespective directed edge and a second node of the respective directededge.

In still other embodiments, the step of assigning a weight to eachdirected edge of the plurality of directed edges in the directedconduction velocity graph can include, for each directed edge, assigninga weight based upon a first peak-to-peak voltage at a first node of therespective directed edge and a second peak-to-peak voltage at a secondnode of the respective directed edge.

In yet further embodiments, the step of assigning a weight to eachdirected edge of the plurality of directed edges in the directedconduction velocity graph can include, for each directed edge, assigninga weight based upon a first cycle length at a first node of therespective directed edge and a second cycle length at a second node ofthe respective directed edge.

In still other embodiments, the step of assigning a weight to eachdirected edge of the plurality of directed edges in the directedconduction velocity graph can include, for each directed edge, assigninga weight based upon a first direction of a first conduction velocityvector assigned to a first node of the respective directed edge and asecond direction of a second conduction velocity vector assigned to asecond node of the respective directed edge.

In yet further embodiments, the step of assigning a weight to eachdirected edge of the plurality of directed edges in the directedconduction velocity graph can include, for each directed edge, assigninga weight based upon one or more of conduction velocity consistency,conduction velocity regularity, electrogram morphological similarity,and contact force.

According to aspects of the disclosure, the step of identifying acardiac activation wavefront using the weighted directed conductionvelocity graph can include: identifying a subset of the plurality ofnodes, through which the cardiac activation wavefront passes;identifying a source node within the subset of the plurality of nodes;and identifying a path of the cardiac activation wavefront, startingwith the source node, through the subset of the plurality of nodes.

In other aspects of the disclosure, the step of identifying a subset ofthe plurality of nodes can include: selecting a seed node within theplurality of nodes; adding the seed node to the subset of the pluralityof nodes; and applying a growing algorithm starting from the seed nodeto add one or more additional nodes to the subset of the plurality ofnodes, wherein the growing algorithm: computes a similarity measurementbetween a first node within the subset of the plurality of nodes and asecond node, adjacent the first node and outside of the subset of theplurality of nodes, and adds the second node to the subset of theplurality of nodes when the similarity measurement satisfies asimilarity criterion. The similarity measurement can be based, at leastin part, upon a direction of a conduction velocity vector assigned tothe first node and a direction of a conduction velocity vector assignedto the second node.

The step of identifying a source node within the subset of the pluralityof nodes can include applying a strongly connected components analysisto the subset of the plurality of nodes.

The step of identifying a path of the cardiac activation wavefront,starting with the source node, through the subset of the plurality ofnodes can include identifying a lowest-cost path, starting with thesource node, through the subset of the plurality of nodes.

It is also contemplated that the method can include: displaying agraphical representation of the geometry; and displaying a graphicalrepresentation of the cardiac activation wavefront on the graphicalrepresentation of the geometry. The step of displaying a graphicalrepresentation of the cardiac activation wavefront on the graphicalrepresentation of the geometry can include animating the graphicalrepresentation of the cardiac activation wavefront on the graphicalrepresentation of the geometry. For example, the graphicalrepresentation of the cardiac activation wavefront can be animated overa time duration based upon a mean cardiac cycle length.

In other aspects of the disclosure, the step of identifying a cardiacactivation wavefront using the weighted directed conduction velocitygraph includes: identifying a first cardiac activation wavefront usingthe weighted directed conduction velocity graph; and identifying asecond cardiac activation wavefront using the weighted directedconduction velocity graph, and wherein the method further includes:displaying a graphical representation of the geometry; displaying agraphical representation of the first cardiac activation wavefront onthe graphical representation of the geometry; and displaying a graphicalrepresentation of the second cardiac activation wavefront on thegraphical representation of the geometry after preset delay time haselapsed following displaying the graphical representation of the firstcardiac activation wavefront.

In still other aspects of the disclosure, the step of identifying acardiac activation wavefront using the weighted directed conductionvelocity graph includes: identifying a first cardiac activationwavefront using the weighted directed conduction velocity graph; andidentifying a second cardiac activation wavefront using the weighteddirected conduction velocity graph, and wherein the method furtherincludes: determining that the first cardiac activation wavefront andthe second cardiac activation wavefront should be merged; merging thefirst cardiac activation wavefront and the second cardiac activationwavefront into a merged cardiac activation wavefront; displaying agraphical representation of the geometry; and displaying a graphicalrepresentation of the merged cardiac activation wavefront; on thegraphical representation of the geometry.

In further aspects of the disclosure, the step of identifying a cardiacactivation wavefront using the weighted directed conduction velocitygraph includes: identifying a source of the cardiac activation wavefrontusing the weighted directed conduction velocity graph; and identifying apath of the cardiac activation wavefront through the weighted directedconduction velocity graph.

Also disclosed herein is a method of mapping cardiac activationwavefronts, including: establishing a mesh including a plurality of meshnodes; assigning each mesh node of the plurality of mesh nodes aconduction velocity vector; defining a plurality of weighted directededges interconnecting the plurality of mesh nodes, thereby creating aweighted directed conduction velocity graph; identifying at least onecardiac activation wavefront using the weighted directed conductionvelocity graph; and displaying the identified at least one cardiacactivation wavefront on a graphical representation of a cardiacgeometry.

The instant disclosure also relates to a system for mapping cardiacactivation wavefronts, including: a cardiac activation wavefrontidentification processor configured: to receive as input a meshcomprising a plurality of mesh nodes and electrophysiology datacomprising conduction velocity data; to assign a conduction velocityvector to each mesh node of the plurality of mesh nodes using theconduction velocity data; to define a plurality of weighted directededges interconnecting the plurality of mesh nodes, thereby creating aweighted directed conduction velocity graph; and to identify at leastone cardiac activation wavefront using the weighted directed conductionvelocity graph; and a mapping processor configured to display theidentified at least one cardiac activation wavefront on a graphicalrepresentation of a cardiac geometry.

The foregoing and other aspects, features, details, utilities, andadvantages of the present invention will be apparent from reading thefollowing description and claims, and from reviewing the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of an electrophysiology system, such as may beused in an electrophysiology study.

FIG. 2 depicts an exemplary multi-electrode catheter used in anelectrophysiology study.

FIG. 3 is a flowchart of representative steps that can be followed tomap a cardiac activation wavefront according to an embodiment of thedisclosure.

FIG. 4a depicts a representative mesh.

FIG. 4b depicts the representative mesh of FIG. 4a with EP data points.

FIG. 4c depicts the representative mesh of FIG. 4a with conductionvelocity vectors at EP data points.

FIG. 4d depicts the assignment of conduction velocity vectors to thenodes of the representative mesh shown in FIG. 4a , referred to hereinas a conduction velocity mesh.

FIG. 5 depicts a representative directed conduction velocity graph.

FIG. 6 illustrates various scenarios in the definition of directed edgesconnecting the nodes of a conduction velocity mesh.

FIG. 7a schematically illustrates a planar cardiac activation wavefront.

FIG. 7b schematically illustrates a rotary cardiac activation wavefront.

FIG. 7c illustrates a shape-dependent weight functions for a rotarycardiac activation wavefront.

FIG. 8 is a flowchart of representative steps that can be followed toidentify a cardiac activation wavefront in a weighted directedconduction velocity graph.

FIG. 9 depicts the identification of a seed node within a weighteddirected conduction velocity graph.

FIGS. 10a-10d illustrate the growth of the seed node identified in FIG.9 into a subset of nodes, through which a cardiac activation wavefrontpasses.

FIG. 11 depicts an approach to displaying cardiac activation wavefrontson a conduction velocity map according to aspects of the instantdisclosure.

DETAILED DESCRIPTION

The present disclosure provides methods, apparatuses, and systems forthe creation of electrophysiology maps (e.g., electrocardiographic maps)including cardiac activation wavefronts.

FIG. 1 shows a schematic diagram of an electrophysiology system 8 forconducting cardiac electrophysiology studies by navigating a cardiaccatheter and measuring electrical activity occurring in a heart 10 of apatient 11 and three-dimensionally mapping the electrical activityand/or information related to or representative of the electricalactivity so measured. System 8 can be used, for example, to create ananatomical model of the patient's heart 10 using one or more electrodes.System 8 can also be used to measure electrophysiology data, including,but not limited to, local activation time (“LAT”), at a plurality ofpoints along a cardiac surface and store the measured data inassociation with location information for each measurement point atwhich the electrophysiology data was measured, for example to create adiagnostic data map of the patient's heart 10.

As one of ordinary skill in the art will recognize, and as will befurther described below, system 8 can determine the location, and insome aspects the orientation, of objects, typically within athree-dimensional space, and express those locations as positioninformation determined relative to at least one reference.

For simplicity of illustration, the patient 11 is depicted schematicallyas an oval. In the embodiment shown in FIG. 1, three sets of surfaceelectrodes (e.g., patch electrodes) are shown applied to a surface ofthe patient 11, defining three generally orthogonal axes, referred toherein as an x-axis, a y-axis, and a z-axis. In other embodiments theelectrodes could be positioned in other arrangements, for examplemultiple electrodes on a particular body surface. As a furtheralternative, the electrodes do not need to be on the body surface, butcould be positioned internally to the body or on an external frame.

In FIG. 1, the x-axis surface electrodes 12, 14 are applied to thepatient along a first axis, such as on the lateral sides of the thoraxregion of the patient (e.g., applied to the patient's skin underneatheach arm) and may be referred to as the Left and Right electrodes. They-axis electrodes 18, 19 are applied to the patient along a second axisgenerally orthogonal to the x-axis, such as along the inner thigh andneck regions of the patient, and may be referred to as the Left Leg andNeck electrodes. The z-axis electrodes 16, 22 are applied along a thirdaxis generally orthogonal to both the x-axis and the y-axis, such asalong the sternum and spine of the patient in the thorax region, and maybe referred to as the Chest and Back electrodes. The heart 10 liesbetween these pairs of surface electrodes 12/14, 18/19, and 16/22.

An additional surface reference electrode (e.g., a “belly patch”) 21provides a reference and/or ground electrode for the system 8. The bellypatch electrode 21 may be an alternative to a fixed intra-cardiacelectrode 31, described in further detail below. It should also beappreciated that, in addition, the patient 11 may have most or all ofthe conventional electrocardiogram (“ECG” or “EKG”) system leads inplace. In certain embodiments, for example, a standard set of 12 ECGleads may be utilized for sensing electrocardiograms on the patient'sheart 10. This ECG information is available to the system 8 (e.g., itcan be provided as input to computer system 20). Insofar as ECG leadsare well understood, and for the sake of clarity in the figures, onlyone lead 6 and its connection to computer system 20 is illustrated inFIG. 1.

A representative catheter 13 having at least one electrode 17 (e.g., adistal electrode) is also depicted in schematic fashion in FIG. 1. Thisrepresentative catheter electrode 17 can be referred to as a“measurement electrode” or a “roving electrode.” Typically, multipleelectrodes on catheter 13, or on multiple such catheters, will be used.In one embodiment, for example, system 8 may utilize sixty-fourelectrodes on twelve catheters disposed within the heart and/orvasculature of the patient.

In other embodiments, system 8 may utilize a single catheter thatincludes multiple (e.g., eight) splines, each of which in turn includesmultiple (e.g., eight) electrodes. Of course, these embodiments aremerely exemplary, and any number of electrodes and catheters may beused. Indeed, in some embodiments, a high density mapping catheter, suchas the EnSite™ Array™ non-contact mapping catheter of St. Jude Medical,Inc., can be utilized.

Likewise, it should be understood that catheter 13 (or multiple suchcatheters) are typically introduced into the heart and/or vasculature ofthe patient via one or more introducers and using familiar procedures.For purposes of this disclosure, a segment of an exemplarymulti-electrode catheter 13 is shown in FIG. 2. In FIG. 2, catheter 13extends into the left ventricle 50 of the patient's heart 10 through atransseptal sheath 35. The use of a transseptal approach to the leftventricle is well known and will be familiar to those of ordinary skillin the art, and need not be further described herein. Of course,catheter 13 can also be introduced into the heart 10 in any othersuitable manner.

Catheter 13 includes electrode 17 on its distal tip, as well as aplurality of additional measurement electrodes 52, 54, 56 spaced alongits length in the illustrated embodiment. Typically, the spacing betweenadjacent electrodes will be known, though it should be understood thatthe electrodes may not be evenly spaced along catheter 13 or of equalsize to each other. Since each of these electrodes 17, 52, 54, 56 lieswithin the patient, location data may be collected simultaneously foreach of the electrodes by system 8.

Similarly, each of electrodes 17, 52, 54, and 56 can be used to gatherelectrophysiological data from the cardiac surface. The ordinarilyskilled artisan will be familiar with various modalities for theacquisition and processing of electrophysiology data points (including,for example, both contact and non-contact electrophysiological mapping),such that further discussion thereof is not necessary to theunderstanding of the conduction velocity mapping techniques disclosedherein. Likewise, various techniques familiar in the art can be used togenerate a graphical representation from the plurality ofelectrophysiology data points. Insofar as the ordinarily skilled artisanwill appreciate how to create electrophysiology maps fromelectrophysiology data points, the aspects thereof will only bedescribed herein to the extent necessary to understand the mapsdisclosed herein.

Returning now to FIG. 1, in some embodiments, a fixed referenceelectrode 31 (e.g., attached to a wall of the heart 10) is shown on asecond catheter 29. For calibration purposes, this electrode 31 may bestationary (e.g., attached to or near the wall of the heart) or disposedin a fixed spatial relationship with the roving electrodes (e.g.,electrodes 17, 52, 54, 56), and thus may be referred to as a“navigational reference” or “local reference.” The fixed referenceelectrode 31 may be used in addition or alternatively to the surfacereference electrode 21 described above. In many instances, a coronarysinus electrode or other fixed electrode in the heart 10 can be used asa reference for measuring voltages and displacements; that is, asdescribed below, fixed reference electrode 31 may define the origin of acoordinate system.

Each surface electrode is coupled to a multiplex switch 24, and thepairs of surface electrodes are selected by software running on acomputer 20, which couples the surface electrodes to a signal generator25. Alternately, switch 24 may be eliminated and multiple (e.g., three)instances of signal generator 25 may be provided, one for eachmeasurement axis (that is, each surface electrode pairing).

The computer 20, for example, may comprise a conventionalgeneral-purpose computer, a special-purpose computer, a distributedcomputer, or any other type of computer. The computer 20 may compriseone or more processors 28, such as a single central processing unit(CPU), or a plurality of processing units, commonly referred to as aparallel processing environment, which may execute instructions topractice the various aspects disclosed herein.

Generally, three nominally orthogonal electric fields are generated by aseries of driven and sensed electric dipoles (e.g., surface electrodepairs 12/14, 18/19, and 16/22) in order to realize catheter navigationin a biological conductor. Alternatively, these orthogonal fields can bedecomposed and any pairs of surface electrodes can be driven as dipolesto provide effective electrode triangulation. Likewise, the electrodes12, 14, 18, 19, 16, and 22 (or any other number of electrodes) could bepositioned in any other effective arrangement for driving a current toor sensing a current from an electrode in the heart. For example,multiple electrodes could be placed on the back, sides, and/or belly ofpatient 11. For any desired axis, the potentials measured across theroving electrodes resulting from a predetermined set of drive(source-sink) configurations may be combined algebraically to yield thesame effective potential as would be obtained by simply driving auniform current along the orthogonal axes.

Thus, any two of the surface electrodes 12, 14, 16, 18, 19, 22 may beselected as a dipole source and drain with respect to a groundreference, such as belly patch 21, while the unexcited electrodesmeasure voltage with respect to the ground reference. The rovingelectrodes 17, 52, 54, 56 placed in the heart 10 are exposed to thefield from a current pulse and are measured with respect to ground, suchas belly patch 21. In practice the catheters within the heart 10 maycontain more or fewer electrodes than the four shown, and each electrodepotential may be measured. As previously noted, at least one electrodemay be fixed to the interior surface of the heart to form a fixedreference electrode 31, which is also measured with respect to ground,such as belly patch 21, and which may be defined as the origin of thecoordinate system relative to which localization system 8 measurespositions. Data sets from each of the surface electrodes, the internalelectrodes, and the virtual electrodes may all be used to determine thelocation of the roving electrodes 17, 52, 54, 56 within heart 10.

The measured voltages may be used by system 8 to determine the locationin three-dimensional space of the electrodes inside the heart, such asroving electrodes 17, 52, 54, 56, relative to a reference location, suchas reference electrode 31. That is, the voltages measured at referenceelectrode 31 may be used to define the origin of a coordinate system,while the voltages measured at roving electrodes 17, 52, 54, 56 may beused to express the location of roving electrodes 17, 52, 54, 56relative to the origin. In some embodiments, the coordinate system is athree-dimensional (x, y, z) Cartesian coordinate system, although othercoordinate systems, such as polar, spherical, and cylindrical coordinatesystems, are contemplated.

As should be clear from the foregoing discussion, the data used todetermine the location of the electrode(s) within the heart is measuredwhile the surface electrode pairs impress an electric field on theheart. The electrode data may also be used to create a respirationcompensation value used to improve the raw location data for theelectrode locations as described in U.S. Pat. No. 7,263,397, which ishereby incorporated herein by reference in its entirety. The electrodedata may also be used to compensate for changes in the impedance of thebody of the patient as described, for example, in U.S. Pat. No.7,885,707, which is also incorporated herein by reference in itsentirety.

In one representative embodiment, the system 8 first selects a set ofsurface electrodes and then drives them with current pulses. While thecurrent pulses are being delivered, electrical activity, such as thevoltages measured with at least one of the remaining surface electrodesand in vivo electrodes, is measured and stored. Compensation forartifacts, such as respiration and/or impedance shifting, may beperformed as indicated above.

In some embodiments, system 8 is the EnSite™ Velocity™ cardiac mappingand visualization system of St. Jude Medical, Inc., which generateselectrical fields as described above, or another localization systemthat relies upon electrical fields. Other localization systems, however,may be used in connection with the present teachings, including forexample, systems that utilize magnetic fields instead of or in additionto electrical fields for localization. Examples of such systems include,without limitation, the CARTO navigation and location system of BiosenseWebster, Inc., the AURORA® system of Northern Digital Inc., Sterotaxis'NIOBE® Magnetic Navigation System, as well as MediGuide™ Technology andthe EnSite™ Precision™ system, both from St. Jude Medical, Inc.

The localization and mapping systems described in the following patents(all of which are hereby incorporated by reference in their entireties)can also be used with the present invention: U.S. Pat. Nos. 6,990,370;6,978,168; 6,947,785; 6,939,309; 6,728,562; 6,640,119; 5,983,126; and5,697,377.

U.S. provisional application No. 62/063,987, filed 15 Oct. 2014 andhereby incorporated by reference as though fully set forth herein,discloses methods, apparatuses, and systems for the creation ofelectrophysiology maps that provide information regarding the localconduction velocity of a cardiac activation wavefront. In such a map(referred to herein as a “CV map,”), it is desirable to be able toidentify different wavefront patterns (e.g., collision, focal, re-entry,rotor). Thus, it is desirable to identify wavefronts, as a group ofconduction velocity vectors, associated with a common source.

One basic methodology of mapping a cardiac activation wavefront usingconduction velocity vector information will be explained herein withreference to the flowchart of representative steps presented as FIG. 3.In some embodiments, for example, the flowchart may represent severalexemplary steps that can be carried out by the computer 20 of FIG. 1(e.g., by one or more processors 28) to identify and map a cardiacactivation wavefront as described herein. It should be understood thatthe representative steps described below can be either hardware- orsoftware-implemented. For the sake of explanation, the term “signalprocessor” is used herein to describe both hardware- and software-basedimplementations of the teachings herein.

A cardiac geometry (that is, a geometry of at least a portion of acardiac surface) is received in block 302. As those of ordinary skill inthe art will appreciate, the cardiac geometry is defined by a pluralityof location points, also referred to herein as “nodes.” These nodes canbe interconnected by edges; together, the collection of nodes and edgesform a mesh that represents the cardiac surface. A representative mesh400, including a plurality of nodes 402, is illustrated in FIG. 4 a.

In some embodiments, the cardiac geometry is acquired using localizationsystem 8. For example, the OneModel™ and/or OneMap™ tools, which arepart of St. Jude Medical's EnSite™ Velocity™ cardiac mapping system, canbe used to create the cardiac geometry. It is also contemplated,however, that the cardiac geometry can be acquired using othermodalities, including, without limitation, MRI, CT, and ultrasoundmapping. Further, insofar as the generation and acquisition of a cardiacgeometry will be familiar to those of ordinary skill in the art, suchthat further explanation thereof is not necessary to the understandingof the cardiac activation wavefront mapping techniques disclosed herein.

According to aspects of the instant disclosure, the relative spacing ofnodes 402 within mesh 400 can be substantially uniform. For example,nodes 402 can be positioned at a user selectable uniform spacing, suchas about 1 mm.

Electrophysiology (“EP”) data for the portion of the cardiac surfacerepresented by the cardiac geometry is received in step 304. EP data canbe collected, for example, using a multi-electrode catheter 13 asdescribed above. As will be familiar to the person of ordinary skill inthe art, and as described above, the EP data describes theelectrophysiological activity occurring on the cardiac surface and caninclude, without limitation, conduction velocity data, local activationtime (“LAT”) data, voltage data (e.g., peak-to-peak voltage data),fractionation data, and cycle length data.

As described above, the ordinarily skilled artisan will be familiar withEP mapping, such that the aspects thereof will only be described hereinto the extent necessary to understand the maps disclosed herein. Forpurposes of illustration only, therefore, aspects of the cardiacactivation wavefront mapping techniques disclosed herein will bedescribed in connection with conduction velocity data, with theunderstanding that it is within the capability of one of ordinary skillin the art to extend these teachings to other EP data.

In some embodiments, the activation wavefront mapping techniquesdisclosed herein are applied to a conduction velocity map, for exampleas disclosed in U.S. provisional application No. 62/063,987. In otherembodiments, however, the EP data (e.g., the received conductionvelocity data) may not map directly to the mesh. That is, the points 404at which the EP data was measured and/or computed (often referred to as“EP data points” or “map points”) may not coincide with the nodes 402 ofthe cardiac geometry 400. FIG. 4b illustrates this situation.

As the person of ordinary skill in the art will appreciate from theinstant disclosure, it is beneficial in this circumstance to assign EPdata to nodes 402 (block 306) using EP data measured at points 404.FIGS. 4c and 4d illustrate one suitable method of assigning conductionvelocity vectors 406 to nodes 402 by interpolating conduction velocitydata 408 measured at points 404, for example by using a Gaussian kernel.

The output of block 306 is referred to herein as a “conduction velocitymesh” (i.e., a collection of nodes 402 including conduction velocityvectors 406). FIG. 4d illustrates a representative conduction velocitymesh 410 generated by assigning data interpolated from conductionvelocity data 408 to nodes 402.

It is contemplated that certain EP data may be excluded when assigningEP data to nodes 402. For example, U.S. provisional application No.62/063,987 discloses a “consistency index” that measures the degree ofconsistency in the direction of the conduction velocity vectorconstituents for a given EP data point over time. A high conductionvelocity consistency index can be associated with a high degree ofdirectional consistency, while a lower conduction velocity consistencyindex can be associated with a low degree of directional consistency(that is, a high degree of randomness in the direction of the conductionvelocity vector constituents). According to aspects of the instantdisclosure, only conduction velocity data from points 404 exhibiting asuitably high consistency index (e.g., having a consistency indexexceeding a preset consistency index threshold, which may be userdetermined) will be included when assigning conduction velocity vectorsto nodes 402.

Likewise, it is contemplated that EP data can be excluded based on othermetrics, such as low voltage or high fractionation.

In block 308, nodes 402 are interconnected by a plurality of directededges. The result of block 308 is referred to herein as a “directedconduction velocity graph.” A representative directed conductionvelocity graph 500, corresponding to the conduction velocity mesh 410shown in FIG. 4d , is illustrated in FIG. 5.

One suitable approach to defining the plurality of directed edges 502interconnecting nodes 402 will now be described with reference to FIG.6, which illustrates four possible directed edge scenarios for any pairof nodes i,j having assigned thereto respective conduction velocityvectors {right arrow over (CV)}_(ι) and {right arrow over (CV)}_(j). Avector {right arrow over (D_(ιj))} is defined that connects node i tonode j, and a vector {right arrow over (D_(jι))} is defined thatconnects node j to node i. {right arrow over (CV)}_(ι) and {right arrowover (D_(ιj))} form an angle Θ_(di). Likewise, {right arrow over(CV)}_(j) and {right arrow over (D_(jι))} form an angle Θ_(dj).

In a first scenario, shown in the upper-left quadrant of FIG. 6, Θ_(di)is less than 90 degrees and Θ_(dj) is greater than or equal to 90degrees. In this scenario, node j is reachable from node i, but not viceversa. Accordingly, a directed edge 502 is defined from node i to nodej.

In a second scenario, shown in the upper-right quadrant of FIG. 6,Θ_(di) is greater than or equal to 90 degrees and Θ_(dj) is less than 90degrees. In this scenario, node i is reachable from node j, but not viceversa. Accordingly, a directed edge 502 is defined from node j to nodei.

In a third scenario, shown in the lower-left quadrant of FIG. 6, Θ_(di)and Θ_(dj) are both less than 90 degrees. In this scenario, each ofnodes i and j is reachable from the other. Accordingly, two directededges, 502 a and 502 b, are defined from node i to node j and from nodej to node i, respectively.

In a fourth scenario, shown in the lower-right quadrant of FIG. 6, bothΘ_(di) and Θ_(dj) are greater than or equal to 90 degrees. In thisscenario, neither node i or j is reachable from the other. Accordingly,no directed edges are defined between nodes i and j.

In block 310, a weight (or cost) is assigned to each directed edge 502.As discussed in further detail below, the weight assigned to a directededge 502 is a measure of the likelihood that the conduction velocityvectors {right arrow over (CV)}_(ι) and {right arrow over (CV)}_(j) atnodes i and j connected by the directed edge 502 result from the samecardiac activation wavefront. That is, the lower the weight, the morelikely that {right arrow over (CV)}_(ι) and {right arrow over (CV)}_(j)result from the same cardiac activation wavefront. The result of block310 is referred to herein as a “weighted directed conduction velocitygraph.”

A weight function W for a directed edge connecting a pair of nodes i,jcan be defined using various metrics. Several suitable weight functionsW will be described in the following paragraphs. It should be understoodthat the exemplary weight functions W described hereinafter can beapplied both individually and in various combinations. In other words,although the representative weight functions described hereinafter arepresented as being functions of only a single metric, it is within thespirit and scope of the instant disclosure to define a weight functionas a function of multiple metrics described herein (e.g., a weightfunction that is both conduction velocity- and time-based).

Conduction Velocity Based Weight Function W_(CV)(i,j).

According to an aspect of the instant disclosure, the weight function Wis based upon the similarity between the conduction velocity vectors{right arrow over (CV)}_(ι) and {right arrow over (CV)}_(j) assigned tonodes i and j, respectively. The angle between these two can be computedaccording to the formula

${\Theta_{i,j} = {\cos^{- 1}\left( \frac{\overset{\rightarrow}{{CV}_{i}} \cdot \overset{\rightarrow}{{CV}_{j}}}{{\overset{\rightarrow}{{CV}_{i}}}{\overset{\rightarrow}{{CV}_{j}}}} \right)}},$and the difference in magnitude can be computed according to the formulad_(i,j)=∥{right arrow over (CV)}_(ι)|−|{right arrow over (CV)}_(j)∥. Theweight function W can be a function of both Θ_(i,j) and d_(i,j), forexample W_(CV)(i,j)=w₁*Θ_(i,j)+w₂*d_(i,j), where w₁ and w₂ are weightingfactors associated with the angle between {right arrow over (CV)}_(ι)and {right arrow over (CV)}_(j) and the difference in magnitude between{right arrow over (CV)}_(ι) and {right arrow over (CV)}_(j),respectively. According to this representative formula, a directed edge502 will have a smaller weight if its nodes i and j have similarconduction velocity vectors (reflecting that similar conduction velocityvectors likely result from the same cardiac activation wavefront).

Time-Based Weight Function W_(t)(i,j).

According to another aspect of the instant disclosure, the weightfunction W is based upon a time required to travel between the two nodesi and j along a directed edge therebetween. This, in turn, can becomputed by dividing the distance between nodes i and j by the velocityalong the directed edge connecting nodes i and j. For example, if thedirected edge runs from node i to node j, then

${W_{t}\left( {i,j} \right)} = {\frac{\overset{\rightarrow}{D_{ij}}}{{\overset{\rightarrow}{{CV}_{i}}\cos\;\Theta_{di}}}\left( {\overset{\rightarrow}{D_{ij}},\overset{\rightarrow}{{CV}_{i}},} \right.}$and Θ_(di) are defined above). According to this representative formula,the weight of a directed edge 502 will be directly proportional to thetime it takes for a wavefront to propagate along that directed edge.

Voltage-Based Weight Function W_(V)(i,j).

In yet another aspect of the instant disclosure, the weight function Wis based upon the similarity between the voltages (e.g., peak-to-peakvoltages) V_(i) and V_(j) at nodes i and j, respectively. For example,W_(V)(i,j)=|V_(i)−V_(j)|. According to this representative formula, adirected edge 502 will have a smaller weight if its nodes i and j havesimilar peak-to-peak voltages (reflecting that similar peak-to-peakvoltages often result from the same cardiac activation wavefront).

Cycle Length-Based Weight Function W_(CL)(i,j).

In still another aspect of the instant disclosure, the weight function Wis based upon the similarity between the cycle lengths CL_(i) and CL_(j)at nodes i and j, respectively. For example,W_(CL)(i,j)=|CL_(i)−CL_(j)|. According to this formula, a directed edge502 will have a smaller weight if its nodes i and j have similar cyclelengths (reflecting that similar cycle lengths often result from thesame cardiac activation wavefront).

Other Suitable Metrics.

Other suitable metrics that can be considered in a weight functioninclude, without limitation, conduction velocity consistency, conductionvelocity regularity, electrogram morphological similarity, contactforce, or combinations thereof. The ordinarily skilled artisan willappreciate how to develop a weight function using these various metrics(e.g., in a manner that computes a lower weight on a directed edge thatinterconnects two nodes likely experiencing the same cardiac activationwavefront).

Shape-Dependent Weight Functions.

The conduction velocity-, time-, voltage-, and cycle length-based weightfunctions described above generally assume a constant model for thecardiac activation wavefront. This model, while appropriate for a planarwavefront, does not hold true for other wavefront patterns (e.g.,rotational wavefronts).

Thus, in some embodiments, different weight functions can be used fordifferent wavefront patterns, such that the weight function isshape-dependent. For purposes of illustration, shape-dependent weightfunctions will be described with reference to conduction velocity vectororientations. It should be understood, however, that shape-dependentweight functions can also be developed for any of the other metricsdiscussed herein (e.g., conduction velocity magnitude, time, voltage,cycle length, conduction velocity consistency, conduction velocityregularity, electrogram morphological consistency, contact force, andthe like).

A conduction velocity vector orientation-based weight function is afunction of Θ_(i,j) (defined above). For a planar wave, such as shownschematically in FIG. 7a , smaller angles Θ_(i) reflect greatersimilarity between the orientations of the respective conductionvelocity vectors assigned to nodes i and j and should therefore yield asmaller weight. Thus, a suitable conduction velocity vectororientation-based weight function for a planar wave can be defined asW_(CV)(ij)=Θ_(i,j).

For a rotational wave such as shown schematically in FIG. 7b , on theother hand, there can be considerable variation in the orientations ofthe conduction velocity vector assigned to the nodes of a directed edgeeven within the same cardiac activation wavefront. The shape-dependentweight function described above for a planar wave would, therefore, givea “false negative” if applied to a rotational wave.

A suitable weight function for a rotational wave, therefore, can be acomparison of two angles between three conduction velocity vectors. Asshown in FIG. 7c , three adjacent nodes i,j, and k have assigned theretorespective conduction velocity vectors {right arrow over (CV)}_(ι),{right arrow over (CV)}_(j), and {right arrow over (CV)}_(k). {rightarrow over (CV)}_(ι) and {right arrow over (CV)}_(j) form an angleΘ_(i,j), while {right arrow over (CV)}_(ι) and {right arrow over(CV)}_(k) form an angle Θ_(k,i).

For a rotational wave, one can expect that the angle with which thewavefront enters a node (e.g., node i) will be similar to the angle withwhich the wavefront exits that node. Smaller weights should therefore beassigned when Θ_(i,j)˜Θ_(k,i). One suitable shape-dependent weightfunction for a rotational wave is, accordingly,W_(CV)(ij)=Θ_(k,i)−Θ_(i,j).

Other weight functions for other wave shapes (e.g., focal, collision)and/or weight functions using additional and/or different metrics (e.g.,conduction velocity magnitude, peak-to-peak voltage, and the like) arealso contemplated.

One or more cardiac activation wavefronts are identified using theweighted directed conduction velocity graph in block 312. Further detailof representative steps that can be included in block 312 are shown inthe flowchart 800 of FIG. 8.

In block 802, a seed node is selected, for example by allowing the userto point-and-click on a graphical representation of the weighteddirected conduction velocity graph. As shown in FIG. 9, in the eventthat the user does not precisely select a node, system 8 can interpretthe user's input to be a selection of the nearest node as the seed node900.

Advantageously, the user's selection of a seed node in block 802 can bearbitrary relative to both the weighted directed conduction velocitygraph and the cardiac activation wavefront to be identified and/ormapped. That is, not only is the user not required to precisely select anode within the weighted directed conduction velocity graph, the user isalso not required to attempt to identify the starting point of a cardiacactivation wavefront. Instead, the methods described herein are appliedto the arbitrarily-selected seed node 900 to identify the starting pointof the cardiac activation wavefront that passes through seed node 900.

According to additional aspects of the disclosure, seed node 900 can beautomatically determined, such as by system 8, instead of by userselection. For example, as described above, nodes 402 can have EP dataassigned thereto (e.g., conduction velocity, cycle length, or the like).This EP data can be used by system 8 as a criterion to identify seednode 900 (e.g., node 402 with the highest conduction velocity, shortestcycle length, or the like).

Seed node 900 is then “grown,” via application of a growing algorithm,to include a subset of the plurality of nodes, through which the samecardiac activation wavefront passes (block 804). The growing algorithmcomputes a similarity measurement SM(i,j) between adjacent nodes i and j(e.g., between seed node 900 and adjacent node 902 in FIG. 9), comparesthe similarity measurement to a similarity criterion (e.g., a similaritythreshold), and adds the adjacent node 902 to the subset of theplurality of nodes if the similarity measurement satisfies thesimilarity criterion (e.g., it exceeds the similarity threshold).

One suitable similarity criterion is based on the angle formed by theconduction velocity vectors of adjacent nodes. If the angle Θ_(i,j)formed by the conduction velocity vectors {right arrow over (CV)}_(ι)and {right arrow over (CV)}_(j) of adjacent nodes i and j is below athreshold angle α, the adjacent node/is added to the subset. If, on theother hand, the angle exceeds the threshold angle α, then the adjacentnode j is not added to the subset.

This is further illustrated in FIGS. 10a-10d . FIG. 10a shows a seednode i and three adjacent nodes labeled p, j, and k. As the person ofordinary skill in the art will appreciate from the foregoing disclosure,the conduction velocity vectors assigned thereto are denoted {rightarrow over (CV)}_(ι), {right arrow over (CV)}_(p), {right arrow over(CV)}_(j), and {right arrow over (CV)}_(k), respectively. Similarly, theangle between {right arrow over (CV)}_(ι) and {right arrow over(CV)}_(j) is denoted Θ_(p,i), the angle between {right arrow over(CV)}_(ι) and {right arrow over (CV)}_(j) is denoted Θ_(i,j), and theangle between {right arrow over (CV)}_(ι) and {right arrow over(CV)}_(k) is denoted Θ_(i,k). Each of Θ_(p,i), Θ_(i,j), and Θ_(i,k) iscompared to a threshold angle α. As shown in FIG. 10b , for each angleless than a (e.g., Θ_(p,i) and Θ_(i,k)), the respective adjacent nodes(e.g., p and k) are added to the subset of nodes, through which thecardiac activation wavefront passes. Node j is not added to the subsetof nodes, through which the cardiac activation wavefront passes, becauseΘ_(i,j)>α. This process can repeat iteratively until all nodes have beenchecked against their adjacent nodes, resulting in the final subset ofnodes, through which the cardiac activation wavefront passes, shown inFIGS. 10c (shaded and circled) and 10 d (extracted from the surroundingexcluded nodes).

Just as different weight functions can be utilized for differentwavefront shapes as described above, so too can different similaritymeasurements be employed without departing from the scope of the instantdisclosure. For example, in some embodiments, the similarity measurementSM(i,j) is identical to W_(CV)(i,j) (i.e., the conduction velocity-basedweight of the directed edge connecting nodes i and j).

Likewise, the similarity measurement can be a function of multiplemetrics. For example, SM(i,j) can be defined as a function of both theconduction velocity-based weight and the cycle length-based weight ofthe directed edge connecting nodes i and j: Θ₁W_(CV)(i,j)+Θ₂W_(CL)(i,j).

In still other embodiments, the growth process is repeated using asecond similarity measurement independent of the first similaritymeasurement.

Once the subset of nodes, through which the cardiac activation wavefrontpasses, is identified, the source node (i.e., the node corresponding tothe origin of the cardiac activation wavefront) is determined in block806. According to aspects of the disclosure, the Strongly ConnectedComponents Analysis (see Sharir, A strong connectivity algorithm and itsapplications to data flow analysis, Computers and Mathematics withApplications 7(1):67-72 (1981); Cormen, Introduction to algorithms(2009), both of which are hereby incorporated by reference as thoughfully set forth herein)) is applied to identify the source node.

In block 808, the path of the cardiac activation wavefront through thesubset of nodes and starting with the source node is identified. Inembodiments disclosed herein, the path of the cardiac activationwavefront is determined by seeking the lowest cost path through thesubset of nodes.

Returning now to FIG. 3, in block 314, the cardiac activation wavefrontcan be displayed, such as on a graphical representation of the cardiacgeometry on display 23. One representative approach to displayingcardiac activation wavefronts is shown in FIG. 11. As shown in FIG. 11,two identified cardiac activation wavefronts 1100, 1102 are shown withtheir corresponding conduction velocity vectors in a different greyscaleon a CV map 1104.

According to another aspect of the disclosure, the cardiac activationwavefront is displayed by sequentially displaying conduction velocityvectors according to their local activation times and local conductionvelocities, starting with the source node identified in block 806 andproceeding along the path identified in block 808.

In some embodiments, the cardiac activation wavefront can be displayedwith animation (e.g., over the mean cycle length of the cardiacactivation), such as by removing or dimming prior conduction velocityvectors as subsequent conduction velocity vectors appear (making itappear as if the conduction velocity vector is moving across thegraphical representation of the cardiac geometry). For example, eachconduction velocity vector can initially illuminate according to itslocal activation time, and can stay illuminated for a time based uponits local conduction velocity.

It is also contemplated to display multiple cardiac activationwavefronts sequentially. For example, if the user identifies three seednodes (or if system 8 is used to automatically identify three seednodes), then three cardiac activation wavefronts can be identified, andthen displayed in sequence, separated by a user-defined delay period.

It is also contemplated that these multiple wavefronts can be sortedand/or prioritized, either manually by a user or automatically accordingto one or more preset criteria. For example, the multiple wavefronts canbe sorted and/or prioritized according to their respective average cyclelengths, their respective average conduction velocities, or the like.Once sorted and/or prioritized, the wavefronts can be displayed insequence as described above (e.g., with a user-defined delay between thedisplay of successively sorted wavefronts).

Those of ordinary skill in the art will also appreciate that a singlecardiac activation wavefront may appear to be multiple cardiacactivation wavefronts if scarring or other blockage interrupts the pathof the cardiac activation wavefront. Thus, in embodiments, multiplecardiac activation wavefronts (e.g., w₁, w₂, . . . , w_(n)) can bemerged into a single cardiac activation wavefront (e.g. w′) by detectingthe blockage (e.g., using low voltage values and fractionatedelectrograms/potentials), identifying the wavefronts that should bemerged, and then merging the wavefronts sequentially (e.g., w₁+w₂→w₂→w′,then w′+w₃→w′, and so forth until all n wavefronts are merged into afinal w′). For example, when merging w₁ and w₂, the final node of w₁ canbe connected to the source node of w₂. Set forth below is one suitablewavefront-merging algorithm:

-   -   Multiple Wavefronts Merge    -   Input: n wavefronts w₁, w₂, . . . , w_(n)    -   Output: the merged wavefronts w′        -   1 Set w′=w_(i)        -   2 For every wavefront        -   3 Identify the connected region R between w_(i) and w′.        -   4 Sort w_(i) and w′ based on the wavefront direction and get            the order of w_(i) and w′        -   5 w′←Combine w_(i), R, w′.        -   6 Reassign the activation time based on the order of w_(i)            and w′

Although several embodiments of this invention have been described abovewith a certain degree of particularity, those skilled in the art couldmake numerous alterations to the disclosed embodiments without departingfrom the spirit or scope of this invention.

For example, although aspects of the disclosure relate to the use of EPdata to map cardiac activation wavefronts, it is contemplated thatnon-EP data can also be used to map cardiac activation wavefronts.Suitable non-EP data includes, without limitation, ultrasound-basedmetrics, MRI based functional images, contact catheter-based cardiacmotion measurements, and other data that provide information about thedirection and speed of different anatomical locations in the heartchamber (e.g., cardiac mechanics, cardiac fluid dynamics, and any otherphysical phenomena representable in a three dimensional field). Theordinarily skilled artisan will appreciate how to adapt and extend theteachings herein to such non-EP data.

As another example, multiple catheters can be used to collect EP datathat can be leveraged according to the teachings herein.

All directional references (e.g., upper, lower, upward, downward, left,right, leftward, rightward, top, bottom, above, below, vertical,horizontal, clockwise, and counterclockwise) are only used foridentification purposes to aid the reader's understanding of the presentinvention, and do not create limitations, particularly as to theposition, orientation, or use of the invention. Joinder references(e.g., attached, coupled, connected, and the like) are to be construedbroadly and may include intermediate members between a connection ofelements and relative movement between elements. As such, joinderreferences do not necessarily infer that two elements are directlyconnected and in fixed relation to each other.

It is intended that all matter contained in the above description orshown in the accompanying drawings shall be interpreted as illustrativeonly and not limiting. Changes in detail or structure may be madewithout departing from the spirit of the invention as defined in theappended claims.

What is claimed is:
 1. A method of mapping a cardiac activationwavefront, comprising: establishing a mesh comprising a plurality ofmesh nodes; assigning each mesh node of the plurality of mesh nodes aconduction velocity vector; defining a plurality of edgesinterconnecting the plurality of mesh nodes, thereby creating aconduction velocity graph; identifying at least one cardiac activationwavefront using the conduction velocity graph; and displaying theidentified at least one cardiac activation wavefront on a graphicalrepresentation of a cardiac geometry.
 2. The method according to claim1, wherein identifying at least one cardiac activation wavefront usingthe conduction velocity graph comprises: identifying a source of the atleast one cardiac activation wavefront using the conduction velocitygraph; and identifying a path of the at least one cardiac activationwavefront through the conduction velocity graph.
 3. The method accordingto claim 2, wherein the conduction velocity graph is weighted, andwherein identifying a path of the at least one cardiac activationwavefront through the conduction velocity graph comprises identifying alowest-cost path through the conduction velocity graph, beginning at thesource of the at least one cardiac activation wavefront.
 4. A method ofmapping a cardiac activation wavefront, comprising: receiving a geometryof at least a portion of a cardiac surface, the geometry comprising aplurality of nodes; receiving conduction velocity data for the portionof the cardiac surface; assigning a conduction velocity vector to eachnode of the plurality of nodes using the conduction velocity data;defining a plurality of edges connecting the plurality of nodes, therebycreating a conduction velocity graph; and identifying a cardiacactivation wavefront using the conduction velocity graph.
 5. The methodaccording to claim 4, wherein identifying a cardiac activation wavefrontusing the conduction velocity graph comprises: identifying a subset ofthe plurality of nodes through which the cardiac activation wavefrontpasses; identifying a source node within the subset of the plurality ofnodes; and identifying a path of the cardiac activation wavefront,starting with the source node, through the subset of the plurality ofnodes.
 6. The method according to claim 5, wherein identifying a subsetof the plurality of nodes comprises: selecting a seed node within theplurality of nodes; adding the seed node to the subset of the pluralityof nodes; and applying a growing algorithm starting from the seed nodeto add one or more additional nodes to the subset of the plurality ofnodes, wherein the growing algorithm utilizes a first similaritymeasurement and a first similarity criterion, and wherein the growingalgorithm: computes the first similarity measurement between a firstnode within the subset of the plurality of nodes and a second node,adjacent the first node and outside of the subset of the plurality ofnodes, and adds the second node to the subset of the plurality of nodeswhen the first similarity measurement satisfies the first similaritycriterion.
 7. The method according to claim 6, wherein the firstsimilarity measurement is based, at least in part, upon a direction of afirst conduction velocity vector assigned to the first node and adirection of a second conduction velocity vector assigned to the secondnode.
 8. The method according to claim 7, wherein the first similaritymeasurement is based, at least in part, upon an angle between thedirection of the first conduction velocity vector and the direction ofthe second conduction velocity vector.
 9. The method according to claim6, wherein the first similarity criterion comprises a maximum anglebetween a direction of a first conduction velocity vector assigned tothe first node and a direction of a second conduction velocity vectorassigned to the second node.
 10. The method according to claim 6,wherein the first similarity measurement is based, at least in part,upon a weight of an edge connecting the first node to the second node.11. The method according to claim 10, wherein the weight comprises aconduction velocity-based weight.
 12. The method according to claim 10,wherein the weight comprises a cycle length-based weight.
 13. The methodaccording to claim 6, wherein the growing algorithm further utilizes asecond similarity measurement and a second similarity criterion, andwherein the growing algorithm: computes the second similaritymeasurement between a first node within the subset of the plurality ofnodes and a second node, adjacent the first node and outside of thesubset of the plurality of nodes, and adds the second node to the subsetof the plurality of nodes when the second similarity measurementsatisfies the second similarity criterion.
 14. The method according toclaim 5, wherein identifying a source node within the subset of theplurality of nodes comprises applying a strongly connected componentsanalysis to the subset of the plurality of nodes.
 15. The methodaccording to claim 5, wherein the conduction velocity graph is weighted,and wherein identifying a path of the cardiac activation wavefront,starting with the source node, through the subset of the plurality ofnodes comprises identifying a lowest-cost path, starting with the sourcenode, through the subset of the plurality of nodes.
 16. The methodaccording to claim 4, further comprising: displaying a graphicalrepresentation of the geometry; and displaying a graphicalrepresentation of the cardiac activation wavefront on the graphicalrepresentation of the geometry.
 17. The method according to claim 4,wherein identifying a cardiac activation wavefront using the conductionvelocity graph comprises: identifying a first cardiac activationwavefront using the conduction velocity graph; and identifying a secondcardiac activation wavefront using the conduction velocity graph.
 18. Asystem for mapping cardiac activation wavefronts, comprising: a cardiacactivation wavefront identification processor configured: to receive asinput a mesh comprising a plurality of mesh nodes and conductionvelocity data; to assign a conduction velocity vector to each mesh nodeof the plurality of mesh nodes using the conduction velocity data; todefine a plurality of edges interconnecting the plurality of mesh nodes,thereby creating a conduction velocity graph; and to identify at leastone cardiac activation wavefront using the conduction velocity graph;and a mapping processor configured to display the identified at leastone cardiac activation wavefront on a graphical representation of acardiac geometry.
 19. The system according to claim 18, wherein thecardiac activation wavefront identification processor is furtherconfigured to identify at least one cardiac activation wavefront usingthe conduction velocity graph by: identifying a source of the at leastone cardiac activation wavefront using the conduction velocity graph;and identifying a path of the at least one cardiac activation wavefrontthrough the conduction velocity graph.
 20. The system according to claim19, wherein the conduction velocity graph is weighted, and whereinidentifying a path of the at least one cardiac activation wavefrontthrough the conduction velocity graph comprises identifying alowest-cost path through the conduction velocity graph, beginning at thesource of the at least one cardiac activation wavefront.